KEYSTONE PRODUCTS

Bill Kemp is an industrial engineer in charge of production planning at Keystone Products. The

company assembles three products from components purchased from outside suppliers. Production

might be limited by market demand, the assembly capacity at several departments, and the availability

of certain critical components.

Market demand during the planning period is limited to 400 units/week of product A, 500

units/week of product B, and 300 units/week of product C. The company has firm contracts with vendors

to supply at least 100 units/week of product A, 150 units/week of product B, and 100 units/week of

product C. The company must produce enough units to meet pre-existing contract, but should not

produce more than the units demanded for any product. Profit contribution has been determined to be

$150/unit on product A, $100/unit on product B, and $200/unit on product C.

Product A requires 5 minutes of assembly time in Shop 1, 4 minutes of assembly time in Shop 2,

and 2 minutes of assembly time in Shop 3. Product B requires 4 minutes in Shop 1, 2 minutes in Shop 2,

and 6 minutes in Shop 4. Product C requires 3 minutes in Shop 1, 4 minutes in Shop 3, and 10 minutes in

Shop 5. The shops work 5 days per week. Shop 1 is able to operate 12 hours per day, Shop 2 is limited to

14 hours per day, Shop 3 is limited to 8 hours per day, Shop 4 is limited to 12 hours per day, and Shop 5 is

limited to 10 hours per day.

Product A uses a special microchip that is limited to 500 chips/week. We will call this Microchip X.

Product B also uses Microchip X. Product B also uses Microchip Y, which is limited to 400 chips/week.

Product C uses a third chip, Microchip Z, which is limited to 600 chips/week.

a.) How many units of each product should be scheduled for production each week, and what would

be the weekly profit?

b.) What constraints are binding? That is, which constraints are at their limit?

c.) Should Kemp consider increasing capacity at any of the shops, and if so, which ones?

d.) Should Kemp consider looking for additional sources of any of the three microchips? If so, which

ones?

e.) Should Keystone's marketing director be urged to promote any of the products more aggressively, to

raise market demand? If so, which ones?

f.) How would your responses to parts a.) and b.) change if the supply of Microchip X was increased by

50%?

g.) How would the responses to parts a.) and b.) change if, in addition to the increase in availability of

Microchip X, the market demand for products A and C both increased by 50%?

h.) How would the responses to parts a.) and b.) change if, in addition to the increase in availability of

Microchip X and the increase in market demand for products A and C, the capacity of Shop 1 was

increased by 50%?